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Longhi S.,CNR Institute for Photonics and Nanotechnologies
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2013

We investigate the onset of parity-time (PT) symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss-gain regions in the presence of an advective term. Similarly to the instability properties of hydrodynamic open flows, it is shown that PT symmetry breaking can be either absolute or convective. In the former case, an initially localized wave packet shows a secular growth with time at any given spatial position, whereas in the latter case the growth is observed in a reference frame moving at some drift velocity while decay occurs at any fixed spatial position. In the convective unstable regime, PT symmetry is restored when the spatial region of gain or loss in the lattice is limited (rather than extended). We consider specifically a non-Hermitian extension of the Rice-Mele tight-binding lattice model, and show the existence of a transition from absolute to convective symmetry breaking when the advective term is large enough. An extension of the analysis to ac-dc driven lattices is also presented, and an optical implementation of the non-Hermitian Rice-Mele model is suggested, which is based on light transport in an array of evanescently coupled optical waveguides with a periodically bent axis and alternating regions of optical gain and loss. © 2013 American Physical Society.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2015

A method for realizing asymmetric (one-way) transmission of discretized light in modulated, linear, and purely passive optical lattices is suggested, which exploits the idea of unidirectional coherent perfect absorption. The system consists of a linear photonic lattice of coupled resonators or waveguides, side coupled to a chain of lossy elements, in which light can avoid the occupation of the dissipative sites when propagating in one way, but not in the opposite one. Non-reciprocity requires modulation of the resonator/waveguide parameters, realizing a dissipative optical Aharonov-Bohm diode with non-reciprocal behavior. © 2015 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2015

Supersymmetric (SUSY) optical structures provide a versatile platform to manipulate the scattering and localization properties of light, with potential applications to mode conversion, spatial multiplexing, and invisible devices. Here we show that SUSY can be exploited to realize broadband transparent intersections between guiding structures in optical networks for both continuous and discretized light. These include transparent crossing of highcontrast- index waveguides and directional couplers, as well as crossing of guiding channels in coupled resonator lattices. © 2015 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2015

In quantum mechanics, the space-fractional Schrödinger equation providesanatural extension of the standard Schrödinger equation when the Brownian trajectories in Feynman path integrals are replaced by Levy flights. Here an optical realization of the fractional Schrödinger equation, based on transverse light dynamics in aspherical optical cavities, is proposed. As an example, a laser implementation of the fractional quantum harmonic oscillator is presentedin which dual Airy beams can be selectively generated under off-axis longitudinal pumping. © 2015 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2012

A scheme for selective coherent destruction of tunneling (CDT) of strongly interacting bosons in a symmetric double-well potential, in which an arbitrarily and a priori prescribed number of bosons are allowed to tunnel from one well to the other one is theoretically proposed. As compared to the many-body CDT scheme recently proposed by Gong, Molina, and Hänggi and based on a fast modulation of the self-interaction strength, the method suggested in this work exploits the traditional method of fast modulation of the energy level unbalance between the two wells by an external ac force. © 2012 American Physical Society.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2014

We suggest a method for trapping photons in quasi-one-dimensional waveguide or coupled-resonator lattices, which is based on an optical analogue of the Aharonov-Bohm cages for charged particles. Light trapping results from a destructive interference of Aharonov-Bohm type induced by a synthetic magnetic field, which is realized by periodic modulation of the waveguide/resonator propagation constants/resonances. © 2014 Optical Society of America


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2014

This Letter shows that bound states in the continuum (BIC), which are normalizable modes with energy embedded in the continuous spectrum of scattered states, exist in certain optical waveguide lattices with PT -symmetric defects. There are two distinct types of BIC modes: BIC states that exist in the broken PT phase, and correspond to exponentially localized modes with either exponentially damped or amplified optical power; and BIC modes with sub-exponential spatial localization that also can exist in the unbroken PT phase. These two types of BIC modes at the PT symmetry breaking point behave differently: in the former case, spatial localization is lost and the defect coherently radiates outgoing waves with an optical power that linearly increases with the propagation distance; in the latter case, localization is maintained and the optical power increase is quadratic. © 2014 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2013

A method to realize effective magnetic fields for photons in square lattices of coupled optical waveguides or resonators is suggested, which is inspired by an optical analogue of photon-assisted tunneling of atom optics. It is shown that an artificial magnetic field can be achieved by application of an index gradient and periodic lumped phase shifts or modulation of the propagation constants/resonances, without the need to modulate the coupling strength. © 2013 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Optics Letters | Year: 2013

Zak phase, that is, the Berry phase acquired during an adiabatic motion of a Bloch particle across the Brillouin zone, provides a measure of the topological invariant of Bloch bands in one-dimensional crystalline potentials. Here a photonic structure, based on engineered lattices of evanescently coupled optical waveguides, is proposed to detect Zak phase difference of photons undergoing Bloch oscillations in topologically distinct Bloch bands of dimerized superlattices. © 2013 Optical Society of America.


Longhi S.,CNR Institute for Photonics and Nanotechnologies
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2015

Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates. © 2015 American Physical Society.

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